Answer:
The simplified value of given expression is 1, which is free from a, therefore the value of the expression does not depend on the variable a.
Step-by-step explanation:
The given expression is
[tex](\frac{5}{a+1}-\frac{3}{a-1}+\frac{6}{a^2-1})\times \frac{a+1}{2}[/tex]
[tex](\frac{5(a-1)-3(a+1)+6}{a^2-1})\times \frac{a+1}{2}[/tex]
[tex](\frac{5a-5-3a-3+6}{a^2-1})\times \frac{a+1}{2}[/tex]
[tex](\frac{2a-2}{a^2-1})\times \frac{a+1}{2}[/tex]
[tex](\frac{2(a-1)}{(a-1)(a+1)})\times \frac{a+1}{2}[/tex]
[tex]\frac{2(a-1)(a+1)}{2(a-1)(a+1)}[/tex]
Cancel out the common factors.
[tex]\frac{2(a-1)(a+1)}{2(a-1)(a+1)}=1[/tex]
Since the simplified value of given expression is 1, which is free from a, therefore the value of the expression does not depend on the variable a.
